1. **State the problem:** In triangle $\triangle DEF$, angle $\angle F$ is a right angle ($90^\circ$). The sides are given as $DF=8$, $FE=15$, and $ED=17$. We need to find the ratio that represents $\tan(\angle D)$.\n\n2. **Recall the tangent definition:** For any angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$. Here, $\angle D$ is one of the acute angles.\n\n3. **Identify sides relative to $\angle D$:**\n- Opposite side to $\angle D$ is side $FE = 15$.\n- Adjacent side to $\angle D$ is side $DF = 8$.\n- Hypotenuse is $ED = 17$.\n\n4. **Write the tangent ratio:**\n$$\tan(\angle D) = \frac{FE}{DF} = \frac{15}{8}.$$\n\n5. **Simplify if possible:** The fraction $\frac{15}{8}$ is already in simplest form.\n\n**Final answer:** $$\boxed{\tan(\angle D) = \frac{15}{8}}.$$